Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
560 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#493 | C2 | semidirect |
| 2. C3×#65362 | C2 | semidirect |
| 3. C3×#64984 | C2 | semidirect |
| 4. C3×C8×#168 | C2 | semidirect |
| 5. #10602069 | C3 | direct (N × H) |
| 14. C5×#493 | C2×C3 | semidirect |
| 15. #65362 | C2×C3 | semidirect |
| 16. #64984 | C2×C3 | semidirect |
| 17. C8×#168 | C2×C3 | semidirect |
| 30. C3×#493 | D5 | semidirect |
| 48. C3×C5×C8 | D8 | semidirect |
| 49. C3×#168 | D8 | semidirect |
| 69. #493 | C3×D5 | semidirect |
| 96. C5×C8 | C3×D8 | semidirect |
| 97. #168 | C3×D8 | semidirect |
| 118. C3×C8 | #686 | semidirect |
| 136. C3×C5 | #1712 | semidirect |
| 157. C8 | C3×#686 | semidirect |
| 162. C5 | C3×#1712 | semidirect |
| 170. C3 | #10602069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C3×#65362 | 2 |
| C3×#64984 | 2 |
| C3×C8×#168 | 2 |
| #10602069 | 3 |
| C3×#1712 | 5 |